Multiple integral inequalities and stability analysis of time delay systems
arXiv:1602.07887 · doi:10.1016/j.sysconle.2016.07.002
Abstract
This paper is devoted to stability analysis of continuous-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple integral inequalities are derived that involve the famous Jensen's and Wirtinger's inequalities, as well as the recently presented Bessel-Legendre inequalities of A. Seuret and F. Gouaisbaut, (2015) and the Wirtinger-based multiple-integral inequalities of M. Park et al. (2015) and T.H. Lee et al. (2015). The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.
References in corpus (3)
- Exponential stability of time-delay systems via new weighted integral inequalities
- Multiple summation inequalities and their application to stability analysis of discrete-time delay systems
- Weighted Orthogonal Polynomials-Based Generalization of Wirtinger-Type Integral Inequalities for Delayed Continuous-Time Systems
Cited by in corpus (4)
- Dissipative delay range analysis of coupled differential-difference delay systems with distributed delays
- A note on relationship between some bounding inequalities in stability analysis of time-delay systems
- General Integral Inequalities Including Weight Functions
- Dissipative analysis of linear coupled differential-difference systems with distributed delays